A pure sample of nuclide X containing N nuclei has an activity A - AQA - A-Level Physics - Question 29 - 2017 - Paper 2

For nuclide X:

• Given, the activity is A and the number of nuclei is N: A = rac{N}{6000}

This indicates that the half-life of nuclide X is 6000 years.

For nuclide Y:

• Given, it contains 3N nuclei and has an activity of 6A. We can set up the equation: 6A = rac{3N}{T_{1/2,Y}}
• Rearranging gives: T_{1/2,Y} = rac{3N}{6A} = rac{1}{2} \cdot \frac{N}{A}
• Since from nuclide X we know that $\frac{N}{A} = 6000$, we substitute: $T_{1/2,Y} = \frac{1}{2} \cdot 6000 = 3000 \text{ years}$

Thus, the half-life of nuclide Y is 3000 years.